Some results on parabolic evolution equations with infinitely many variables
The author considers the problem (*) \(\Phi_ t=(1/2)Tr(S\Phi_{xx})\), \(\Phi (0,x)=\Phi_ 0(x)\) with S denoting a nuclear positive operator on a separable Hilbert space H, \(\Phi\) being a mapping (0,\(\infty)\times H\to R\) and Tr denoting the trace. Problems of this tpye are of importance in probability theory. The author then proves existence and uniqueness results in problem (*) and extensions of it.
scientific article; zbMATH DE number 4021735
scientific article